Josephood7

If AA is the area of a circle with radius rr and the circle expands as time passes, find dA/dtdA/dt in terms of dr/dtdr/dt. Below, use "s" for dr/dtdr/dt.

(b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1m/s1m/s, how fast must the area of the spill increasing when the radius is 22m22m?

(a) dA/dt=dA/dt= 
(b) dA/dt=dA/dt= 

A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward first base with a speed of 20 ft/s.

At what rate is his distance from second base changing when he is halfway to first base?
Answer =  ft/s

At what rate is his distance from third base changing at the same moment?
Answer = 

Two carts, A and B, are connected by a rope 39ft39ft long that passes over a pulley PP. The point QQ is on the floor 12ft12ft directly beneath PP and between the carts. Cart A is being pulled away from QQ at a speed of 2ft/s2ft/s.
How fast is cart B moving toward QQ at the instant when cart A is 5ft5ft from QQ?

A runner sprints around a circular track of radius 100m100m at a constant speed of 7m/s7m/s. The runner's friend is standing at a distance 200m200m from the center of the track. How fast is the distance between the friends changing (can be interpreted as either increasing or decreasing depending on the perspective) when the distance between them is 200m200m?

The minute hand on a watch is 8mm8mm long and the hour hand is 4mm4mm long. How fast is the distance between the tips of the hands changing at one o'clock? Round your answer to the nearest tenth.